Constructs a corrective learning system using the Socratic dialogue as a guide to correct mistakes in students' knowledge of subtraction. The Socratic dialog applies a dialectic method to present questions to the student and lets the student reconsider his or her own thinking. Results show that the Socratic-dialog approach is of great help to…

Describes how the card game Numero helps students improve their knowledge of basic number facts while having fun. Suggests ways in which Numero can best be used in the classroom. (ASK)

This study investigated the developmental paths of Japanese Grade 1 students' understanding of quantities through the examination of their addition solution methods over the school year period. The individual students exhibited a wide range of experiences with and knowledge of addition from the beginning to the end of the school year. Students…

In this paper I argue that children have a right to basic numeracy and that studies of adult numeracy suggest that this right is being denied to many in British schools. Because of the way that maths education discourses are structured, we do not have a separately defined discourse around numeracy teaching, and this has implications for young…

Traditionally, primary schools place minimal emphasis upon relations and transformations as objects of study. In their research, the authors have found the young children can engage in conversations about equivalence and equations (Warren & Cooper, 2005a) and functional thinking (Warren & Cooper, 2005b). Fundamental to relations and…

A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with…

The What Works Clearinghouse (WWC) looked at elementary school math curricula designed to promote math knowledge and skills among elementary school students (average ages 5 to 10 years). Curricula included in this review are replicable, materials-based instructional programs that cover one or more of the following content areas: numbers,…

The first four chapters of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…

Chapters 11 through 14 of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…

Guidelines are presented for modifying basic instruction of subtraction facts for elementary level learning disabled students. A detailed case study is used to illustrate a five-step structured program: (1) find a way to work it out; (2) add to check; (3) learn the partner facts; (4) study families of facts; (5) review and practice. The selection…

Ways in which the emerging field of cognitive science can have a major impact on practical education are demonstrated by an overview of two projects: the work on Socratic tutoring by Collins and Stevens, and the diagnosing students' misconceptions in arithmetic by Brown and Burton. These two projects are cited as examples of how the techniques of…

The Tucson Early Education Program is working with "orchestrated instruction," a cooking experience which is an experimental attempt to pull together the various components of early education. Individual subskills such as arithmetic and language arts are learned for a larger project that the children are interested in, and skills are developed as…

Presents ideas for teaching basic skills. Includes strategies for teaching about human rights, directions for making an adding machine to use in addition and subtraction drill, activities for developing effective discussion skills, and suggestions for teaching place-name geography. (JMB)

An approach to solving many linear programming problems, using only arithmetical thinking in conjunction with the usual diagram, is given. (MN)

Presented is a paradigm for teaching basic and semibasic arithmetic facts to children with arithmetic difficulties, in which the student progresses from the use of concrete materials such as blocks, to the use of diagrams such as tally marks, to a reasoning process, to responding in an automatic manner. (DLS)